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1 Vol. 2 No (Mar. 2009) Effect of Overconfidencial Investor to Stock Market Behaviour Ryota Inaishi, 1 Fei Zhai 1 and Eisuke Kita 1 Recently, the behavioral finance theory has been interested in order to explain from the investor s psychology the phenomenon that cannot be explained by a finance theory based on the efficient market hypothesis. In this research, we focus on the overconfidence, one of many psychological bias, and analyze the effect of overconfident investors to the stock market by the multi agent simulation. As a result, we found that, according to the increase of overconfident investors in the market, the market dealing increases and the rising trend tends to be seen more often. Moreover, the analysis of the relation between the overconfidence and the rising trend reveals that the rising trend makes the investors more overconfident. 1 Graduate School of Information Sciences, Nagoya University 1. 1),2) 3),4) 5) 1 Shleifer 3) Barber 45% 6),7) 1 1 8) 1 1 9) 4),5) 9) 10 c 2009 Information Processing Society of Japan

2 11 9) Daniel 10) 2. Fama 11) ) ) 13) Shleifer 14) 4) )

3 ),5) 5) 4) Nick Leeson 15) Nick Leeson Belsky 16) 9) α 1 Fig. 1 Multi-layeared perceptron. 0 <α<1 α =0.5 (1) (2) (3) (4) (5) (5) ) 1 hidden output 3 multi-layered perceptron MLP MLP j

4 13 y j = f(η j θ j) (1) n η j = x iω ij (2) i=1 x i ω ij i j θ j f 1 f(η) = (3) 1 + exp( η) n n =1, 2, 3,, 20 MA n MA t = Pt 1 + Pt Pt n k n k (4) k P n k MA k t x teacher x teacher MLP ω θ ) (1) ω (2) x i teacher i i =1, 2,,n (3) x i y output i teacher i E = y output i teacher i 2 (5) (4) ω E ω ω ɛ E (6) ω (5) (2) (6) ɛ ɛ k t Pt k Pt k = F ( x) (7) x =(MA k t,ma k t 1,,MA k t l+1) (8) x l t n k MA k t F 3.3 α 0 <α<1 α = n =20 P σ h σ h = 1 n (u t ū) n (9) ū = 1 n t=1 n u t (10) t=1 u t =log Pt (11) P t ),9) σ s σ s =(1.5 α) σ h (12)

5 14 α (12) α 1 α S t M t 2 Q t Capital asset pricing model CAPM Sharpe ( )/ P t MA t σ s P t >MA t Pt Pt 1 /Pt 1 Q t =(M t/p t) (13) σ s P t <MA t Q t = S t P t P t 1 /P t 1 σ s (14) Zhai 21) (13) (14) S t+1 = S t + Q t (15) M t+1 = M t P t Q t (16) S t+1 = S t Q t (17) M t+1 = M t + P t Q t (18) Q t P t P t α (1) P t (2) Pt Pt ξ = a a s (3) (19) α f(f(α)+ξ) (20) (20) f (3) f a a a =0.1 (19) s p =1/20 p =0.1 (1 α) (21) p (21) α =0.5 p =0.05 = 1/20

6 15 Fig. 2 2 Demand-supply curve. 3 TOPIX2006 Fig. 3 TOPIX ),9) Black 18) Black TOPIX Fig. 4 Prediction of agent for real stock price with 5 days moving average and 20 days moving average ),9) 5000 ɛ =

7 16 Fig Price history in market1. Fig Price history in market Fig. 7 Fig Price history in market Price history in market4.

17 Fig. 9 9 5 Price history in market5. 11 Fig.

10 History of average order amount in case of no rising trend. Fig.

8 17 Fig Price history in market5. 11 Fig. 11 History of average order amount in case of rising trend. 10 Fig. 10 History of average order amount in case of no rising trend. Fig Volume of dealing of average 20 times in 5 markets Buy Sell

9 18 13 Fig. 13 Price history Fig. 14 Price history in market α =0.9 p =1/ ),19) 12),19) α 3

10 Fig. 15 Price history in market Fig. 17 Frequency distribution of volatility in 5 markets (No rising trend) Fig. 16 Price history in market3. Fig Frequency distribution of volatility in maket4 and market5 (Rising trend). 1 Table 1 Marke Frequency of rising trend. Frequency of rising trend V olatility = P (t) P (t 1) P (t 1) 100 (22) Karpoff

11 Table 2 Each agent s overconfidence after market5 ends of 100 periods. Market s state Average of overconfidence. Ratio of agent of overconfidence over 0.9.(%) No rising trend Rising trend Fig. 19 History of volume of dealing in market5. Volatility 20)

21 1) Shefrin, H., Greed, B. and Fear: Finance and the Psychology of Investing, Oxford University Press (2002). 2) (2001). 3) Shleifeer, A.: Ineffect Markets, Oxford University Press (2000).

and Odean, T.: Online Investor: Do the slow Die Fast, Review of Financial Studies, Vol.15, pp.455 487 (2002). 8) (2003). 9) Vol.47, No.5, pp.1433 1441 (2006). 10) Dniel, K., Hirshleifer, D.

: Efficient capital markets: A review of theory and empirical work, Journal of Finance, Vol.25, pp.383 417 (1970). 12) & (2005). 13) Freidman, M.

12 21 1) Shefrin, H., Greed, B. and Fear: Finance and the Psychology of Investing, Oxford University Press (2002). 2) (2001). 3) Shleifeer, A.: Ineffect Markets, Oxford University Press (2000). 4) (2003). 5) (2001). 6) Barber, B. and Odean, T.: Boys will be Boys: Gender, Overconfidence and Common Stock Investment, Quartery Journal of Economics, Vol.116, pp (2001). 7) Barber, B. and Odean, T.: Online Investor: Do the slow Die Fast, Review of Financial Studies, Vol.15, pp (2002). 8) (2003). 9) Vol.47, No.5, pp (2006). 10) Dniel, K., Hirshleifer, D. and Subrahmanyam, A.: Investor Psychology and Security Market Under Overreactions, Journal of Finance, Vol.53, pp (1998). 11) Fama, E.: Efficient capital markets: A review of theory and empirical work, Journal of Finance, Vol.25, pp (1970). 12) & (2005). 13) Freidman, M.: Essays in Positive Economics, University of Chicago Press (1953). 14) Shleifer, A. and Vishny, R.W.: The Limits of Arbitrage, Journal of Finance, Vol.52, No.1, pp (1997). 15) N. (1997). 16) G. T. (2000). 17) (1998). 18) Black, F.: Noise, Journal of Finance, Vol.41, pp (1986). 19) (2003). 20) Karpoff, J.: The Relation between Price Change and Trading Volume: A Survey, Journal of Financial and Quantitative Analysis, Vol.22, pp (1987). 21) Zhai, F., Shen, K., Vol.47, No.SIG14(TOM15), pp (2006) ( ) ( ) ( ) Cellular Automata Trefftz IEEE ISBE

130 Oct Radial Basis Function RBF Efficient Market Hypothesis Fama ) 4) 1 Fig. 1 Utility function. 2 Fig. 2 Value function. (1) (2)

130 Oct Radial Basis Function RBF Efficient Market Hypothesis Fama ) 4) 1 Fig. 1 Utility function. 2 Fig. 2 Value function. (1) (2) Vol. 47 No. SIG 14(TOM 15) Oct. 2006 RBF 2 Effect of Stock Investor Agent According to Framing Effect to Stock Exchange in Artificial Stock Market Zhai Fei, Shen Kan, Yusuke Namikawa and Eisuke Kita Several